It is based on a design by American firearms inventor John Browning, and completed by Dieudonné Saive at Fabrique Nationale (FN) of Herstal, Belgium. Browning died in 1926, several years before the design was finalized. The Hi-Power is one of the most widely used military pistols in history, having been used by the armed forces of over 50 countries.

The Hi Power name is somewhat misleading and alluded to the 13-round magazine capacity; almost twice that of contemporary designs such as the Luger P08 or Mauser 1910. The Browning was one of the first, if not the first, pistols to utilize a double-stack magazine with ten or thirteen round capacities, thus making it more high-powered than pistols with single-stack magazines, like the 1911, which is what the Hi-Power is partly based off of. However, despite the Hi-Power being a single-action firearm, it had a heavy trigger pull, almost ten pounds, which is far heavier than that of the 1911, which was less than four pounds.

The pistol is often referred to as an HP (for "Hi-Power" or "High-Power") or as a GP (for the French term, "Grande Puissance"). The terms P-35 and HP-35 are also used, based on the introduction of the pistol in 1935. It is most often called the "Hi Power", even in Belgium. Other names include BAP (Browning Automatic Pistol), particularly in Irish service, or BHP (Browning High-Power).